MC ▸ NA ▸ courses ▸ NUMA12 – Spring 2012

In short

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(If necessary Tuesday 10-12 in MH:332B)
Wednesday 13-15 in MH:333 (but 29/2 in MH:332A)
Friday 15-17 in MH:332B
(MH=Mathematics house)

Thematic Schedule

DateLectureProtocol
2012-01-25

Concept of best approximation, norms.

Lecture 1
2012-01-27

Uniqueness of best approximations, the best approximation operator. The Lebesgue constant.

Lecture 2
2012-02-01

Piecewise polynomial approximations. Lagrange polynomials. Interpolation error.

Lecture 3
2012-02-03

Chebyshev polynomials. The Lebesgue constant of the Lagrange interpolation operator.

Lecture 4
2012-02-06

Splines.

Lecture 14
2012-02-08

Divided differences. The Newton form. Hermite interpolation.

Lecture 5
2012-02-10

The Weierstrass theorem. Bernstein polynomials. Montonic Operators.

Lecture 6
2012-02-15

Minimax Approximation, Haar spaces, Characterization Theorem.

Lecture 7
2012-02-17

The exchange algorithm.

Lecture 8
2012-02-22

Convergence of the exchange algorithm.

Lecture 9
2012-02-24

Least squares approximation

Lecture 10
2012-02-28

The best L1 approximation.

Lecture 11
2012-02-29

Orthogonal polynomials. The L2-norm and the minimax approximation of polynomials.

Lecture 12
2012-03-02

Discrete L1 approximation.

Lecture 13